1,601,832 research outputs found

    Quantum Baker Maps for Spiraling Chaotic Motion

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    We define a coupling of two baker maps through a pi/2 rotation both in position and in momentum. The classical trajectories thus exhibit spiraling, or loxodromic motion, which is only possible for conservative maps of at least two degrees of freedom. This loxodromic baker map is still hyperbolic, that is, fully chaotic. Quantization of this map follows on similar lines to other generalized baker maps. It is found that the eigenvalue spectrum for quantum loxodromic baker map is far removed from those of the canonical random matrix ensembles. An investigation of the symmetries of the loxodromic baker map reveals the cause of this deviation from the Bohigas-Giannoni-Schmit conjecture

    Sheaves and Duality in the Two-Vertex Graph Riemann-Roch Theorem

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    For each graph on two vertices, and each divisor on the graph in the sense of Baker-Norine, we describe a sheaf of vector spaces on a finite category whose zeroth Betti number is the Baker-Norine "Graph Riemann-Roch" rank of the divisor plus one. We prove duality theorems that generalize the Baker-Norine "Graph Riemann-Roch" Theorem

    A Baker–Venkataraman retro-Claisen cascade delivers a novel alkyl migration process for the synthesis of amides

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    A simple extension of the carbamoyl Baker-Venkataraman rearrangement has been developed. If residual water in the reaction is not strictly excluded a Baker-Venkataraman retro-Claisen cascade takes place, giving amide products, in which an alkyl group apparently migrates between two functionalities of the substrate

    Organic barley producers' desired qualities for crop improvement

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    Barley fits well into many different organic farming systems. It can be grown as either a winter or spring annual crop in many temperate regions. Barley can be used for food, malting, or animal feed, providing growers with diverse marketing opportunities. Despite its advantages, many organic farmers in the USA have not adopted barley as a regular crop in their rotation. Researchers surveyed organic barley producers to discover what they considered to be the main obstacles to growing barley. The primary obstacles identified were limited markets and price. Breeding and development of high-quality barley suitable for organic systems and specialty markets may be a way to expand markets and secure a better price. Farmers identified yield as the most important agronomic trait of interest, but other traits such as nutritional quality were also highly ranked. Naked (hull-less) barley bred for multi-use quality is a possible alternative that allows organic farmers to sell into multiple markets. Most respondents expressed interest in the development of such varieties suitable for organic farming conditions. The researchers conducted follow-up interviews to obtain detailed information on how barley is used in organic farming systems, production practices, costs of production, and what traits farmers would like to see breeders focus on

    Baker-Akhiezer functions and generalised Macdonald-Mehta integrals

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    For the rational Baker-Akhiezer functions associated with special arrangements of hyperplanes with multiplicities we establish an integral identity, which may be viewed as a generalisation of the self-duality property of the usual Gaussian function with respect to the Fourier transformation. We show that the value of properly normalised Baker-Akhiezer function at the origin can be given by an integral of Macdonald-Mehta type and explicitly compute these integrals for all known Baker-Akhiezer arrangements. We use the Dotsenko-Fateev integrals to extend this calculation to all deformed root systems, related to the non-exceptional basic classical Lie superalgebras.Comment: 26 pages; slightly revised version with minor correction

    Quantum baker maps with controlled-NOT coupling

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    The characteristic stretching and squeezing of chaotic motion is linearized within the finite number of phase space domains which subdivide a classical baker map. Tensor products of such maps are also chaotic, but a more interesting generalized baker map arises if the stacking orders for the factor maps are allowed to interact. These maps are readily quantized, in such a way that the stacking interaction is entirely attributed to primary qubits in each map, if each subsystem has power-of-two Hilbert space dimension. We here study the particular example of two baker maps that interact via a controlled-not interaction. Numerical evidence indicates that the control subspace becomes an ideal Markovian environment for the target map in the limit of large Hilbert space dimension.Comment: 8 page

    Bispectrality for deformed Calogero-Moser-Sutherland systems

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    We prove bispectral duality for the generalized Calogero-Moser-Sutherland systems related to configurations An,2(m),Cn(l,m)A_{n,2}(m), C_n(l,m). The trigonometric axiomatics of Baker-Akhiezer function is modified, the dual difference operators of rational Macdonald type and the Baker-Akhiezer functions related to both series are explicitly constructed.Comment: 45 page
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